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If one guitar string is tuned to a frequency of 440 Hz and a string on another guitar produces 6 beats per second when played together with the first string, what are the possible frequencies of the... A certain rope has a length of 8 m and a mass of 2.4 kg. It is fixed at one end and held taut at the other with a tension of 30 N. The end of the rope is moved up and down with a frequency of 2.5 Hz.... An insect is embedded inside a glass block (n = 1.5) so that it is located 2.4 cm below a plane surface of the block. How far from this surface does this insect appear to a person looking at the... With your friends, whirl a bucket of water in a vertical circle fast enough so the water doesnt spill out. As it happens, the water in the bucket is falling, but with less speed than you give to the... What are three lines of evidence supporting cosmic inflation? In contact metamorphism, water-rich, low-melting temperature minerals are found far away from the contact zone. Give two examples of such minerals. Identify the following functional groups in this organic molecule: amide, ester, ketone, ether, alcohol, aldehyde, amine. What is a fossil? How are fossils used in the study of geology? Darcys law gives us the volume flow ratevolume per time (for example, cubic meters per day, m 3 /day). Another way to express volume is on a per-unit-area basis. For example, if we have a 1-m 3 cube,... In a sequence of sedimentary rock layers, the oldest layer is on the bottom and the youngest layer is at the top. What relative dating principle applies here? How old are the oldest rocks on Earth? About how old are the oldest rocks on the Moon? The nearest star to our Sun is Alpha Centauri, which is about 4.4 light-years away. Assume that it too has an Oort cloud about 1.6 light-years in diameter. Show that there is enough space between us... A residential photo voltaic installation is described as producing 5000 kilowatt hours per year. What is a kilowatt hour per year in SI units? What might be the purpose of using kWh/y rather than the... What is the rationale for modeling combustion as a constant pressure process in the Diesel cycle when it was modeled as constant volume in the Otto cycle? Explain in words what is going on in the Rankine reheat cycle of Figure 13.16(a) and, referring to the figure, explain the statements made at the end of the discussion in the text about the... Gravity is a long-range force proportional to the masses of the interacting bodies. Physicists have long searched to see if there might be a long-range force that is proportional to baryon number.... Compute the ShockleyQueisser bound on V oc for a silicon cell with band gap 1.1 eV at temperature T = 300 K. Model the Sun as a black body at 6000 K. Compute the momentum of an electron with kinetic energy 2 eV and compare to the momenta of a photon with the same energy. Explain why such a photon cannot excite an electron in silicon without... Explain why petroleum is currently the primary source of fuel for land and air transport, while coal is the primary fuel for electric power plants. In 35.3.3 we remarked that the fact that ice floats in seawater has far-reaching consequences for climate and life on Earth. Discuss what Earths surface might look like if ice did not float. Estimate the thermodynamic limit on the 1st law efficiency of a device that turns heat radiation from a wood fire into electricity. When you turn on a powerful motor in your home, such as an air conditioner compressor, you will notice the incandescent lights dim briefly. Explain why. Using the results of Problem 1.7, show that de r / d = e and de /d = e r . Data From Problem 1.7 Show that the unit vectors e r and e in a cylindrical coordinate system are related to the unit... A pipeline containing natural gas from a hydraulic fracturing process contains 80% methane gas (CH 4 , species A) and 20% ethane (C 2 H 6 , species B) gas at 3.0 atm and 17 C, as shown in figure... A process is being developed to produce carbonated beverages. As part of this process, a packed-bed absorption tower will be used to dissolve carbon dioxide, CO 2 , gas into water. Pure mountain... Show that a small change in the reduced mass of the electron produces a small change in a spectral line given by / = /. Use this to calculate the difference in the Balmer red line = 656.3 nm... An atom in an excited state will on the average undergo a transition to a state of lower energy in about 10 -8 seconds. If the electron in a doubly ionized lithium atom (Li +2 , which is... In a particular x-ray tube, an electron approaches the target moving at 2.25 x 10 8 m/s. It slows down on being deflected by a nucleus of the target, emitting a photon of energy 32.5 keV. Ignoring... The orbiting space shuttle moved around Earth well above 99 percent of the atmosphere, yet it still accumulated an electric charge on its skin due, in part, to the loss of electrons caused by the... What must be the kinetic energy of an electron if the ratio of its de Broglie wavelength to its Compton wavelength is (a) 10 2 , (b) 0.2, and (c) 10 -3 ? If a rigid body has moment of inertia I and angular velocity , its kinetic energy is where L is the angular momentum. The solution of the Schrdinger equation for this problem leads to quantized... The value of the constant C 200 in Equation 7-33 is Find the values of (a) , (b) 2 , and (c) The radial probability density P(r) at r = a 0 for the state n = 2, = 0, m = 0 in hydrogen. Give your... (a) What is the ratio of the number of particles per unit area on the screen scattered at 10 to those at 1? (b) What is the ratio of those scattered at 30 to those at 1? Compute the normalization constant C 210 in Equation 7-34. 210 = C210e-Zr/2an cos 0 ao 7-34 FIGURE EX2.5 shows the position graph of a particle. a. Draw the particles velocity graph for the interval 0 s £ t £ 4 s. b. Does this particle have a turning point or points? If so, at... Does the object represented in FIGURE Q1.4 have a positive or negative value of α x ? Explain. Figure Q1.4 A speed skater accelerates from rest and then keeps skating at a constant speed. Draw a complete motion diagram of the skater? A car travels to the left at a steady speed for a few seconds, then brakes for a stop sign. Draw a complete motion diagram of the car? A Porsche accelerates from a stoplight at 5.0 m/s 2 for five seconds, then coasts for three more seconds. How far has it traveled? Draw a complete pictorial representation. Do not solve these... Alan leaves Los Angeles at 8:00 a.m. to drive to San Francisco, 400 mi away. He travels at a steady 50 mph. Beth leaves Los Angeles at 9:00 a.m. and drives a steady 60 mph. a. Who gets to San... A rock is dropped from the top of a tall building. The rocks displacement in the last second before it hits the ground is 45% of the entire distance it falls. How tall is the building? A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.0 s later. What was the rockets... The minute hand on a watch is 2.0 cm in length. What is the displacement vector of the tip of the minute hand a. From 8:00 to 8:20 A.M.? b. From 8:00 to 9:00 A.M.? A pine cone falls straight down from a pine tree growing on a 20 slope. The pine cone hits the ground with a speed of 10 m/s. What is the component of the pine cones impact velocity (a) Parallel to... For a projectile, which of the following quantities are constant during the flight: x, y, r, v x , v y , v, a x , a y ? Which of these quantities are zero throughout the flight? You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground.... A rifle is aimed horizontally at a target 50 m away. The bullet hits the target 2.0 cm below the aim point. a. What was the bullets flight time? b. What was the bullets speed as it left the barrel? Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the... A bicycle wheel is rotating at 50 rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.50 rad / s2. a. What is the wheels angular velocity, in rpm, 10 s... Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decelerates to a halt in 2.0 s. How many revolutions does it make? A rubber ball is dropped onto a ramp that is tilted at 20°, as shown in FIGURE P4.59. A bouncing ball obeys the law of reflection, which says that the ball leaves the surface at the same angle it... Evaluate the matrix [B] for the quadratic quadrilateral element shown in Figure 1015 on page 521 (Section 10.5). (a) (b) 3. (20, 15) (12, 15) (10, 10)- (20, 10) (20, 20) (12, 16) (10, 10) (20, 10) In Fig. P5.68 m 1 = 20.0 kg and α = 53.1 o . The coefficient of kinetic friction between the block and the incline is μ k = 0.40. What must be the mass of the hanging... Consider the system shown in Fig. P6.86. The rope and pulley have negligible mass, and the pulley is frictionless. Initially the 6.00-kg block is moving downward and the 8.00-kg block is moving to... A 350-kg roller coaster starts from rest at point A and slides down the frictionless loop-the-loop shown in Fig. P7.45. (a) How fast is this roller coaster moving at point B? (b) How hard does it... The position of a squirrel running in a park is given by r = [(0.280 m/s)t + (0.0360 m/s 2 )t 2 ]i + (0.0190 m/s 3 )t 3 j. (a) What are and u x (t) and u y (t), the x- and y-components of the... A wheel is turning about an axis through its center with constant angular acceleration. Starting from rest, at t = 0, the wheel turns through 8.20 revolutions in 12.0 s. At t = 12.0 s the kinetic... Two uniform solid spheres, each with mass and radius R = 0.0800 m, are connected by a short, light rod that is along a diameter of each sphere and are at rest on a horizontal tabletop. A spring with... The point of the needle of a sewing machine moves in SHM along the x-axis with a frequency of 2.5 Hz. At t = 0 its position and velocity components are +1.1 cm 15 cm/s. and respectively. (a) Find the... A small block is attached to an ideal spring and is moving in SHM on a horizontal, friction less surface. When the block is at x = 0.280 m, the acceleration of the block is 5.30 m/s 2 . What is the... A continuous succession of sinusoidal wave pulses are produced at one end of a very long string and travel along the length of the string. The wave has frequency 70.0 Hz, amplitude 5.00 mm, and... A bat flies toward a wall, emitting a steady sound of frequency 1.70 kHz. This bat hears its own sound plus the sound reflected by the wall. How fast should the bat fly in order to hear a beat... A copper pot with a mass of 0.500 kg contains 0.170 kg of water, and both are at a temperature of 20.0C. A 0.250-kg block of iron at 85.0C is dropped into the pot. Find the final temperature of the... In a container of negligible mass, 0.200 kg of ice at an initial temperature of 40.0 o C is mixed with a mass m of water that has an initial temperature of 80.0 o C. No heat is lost to the... Two rods, one made of brass and the other made of cop-per, are joined end to end. The length of the brass section is 0.200 m and the length of the copper section is 0.800 m. Each segment has... Solve this ODE using a Symbolic software program: All initial conditions for y and its derivatives are zero. d'y dy + 16y 176 + 105y = 1 + 86y dt? dr dt di3 dt Can a tank with the outflow rate fixed by a constant speed pump reach a steady state if the inlet flow rate undergoes a step change? Why, or why not? If the transfer function is G(s) = K/s, is it... Consider the transfer function (a) What are the gain, time delay, time constants, poles, and zeros of G(s)? (b) Will the step response of this transfer function exhibit (i) inverse response or (ii)... The output response data y shown in Table E7.9 were generated from a step change in input u from 1 to 5 at time t = 0. Develop a transfer function model of the form Y(s) Ke-0s (T,8 +1)(t,s + 1) U(s)... For the following statements, discuss whether they are always true, sometimes true, always false, or sometimes false. Cite evidence from this chapter. (a) Increasing the controller gain speeds up the... The following data were collected from a cell concentration sensor measuring absorbance in a biochemical stream. The input u is the flow rate deviation (in dimensionless units) and the sensor output... An electronic PID temperature controller is at steady state with an output of 12 mA. The set point equals the nominal process temperature initially. At t = 0, the error signal is increased at the... What differential equation model represents the parallel PID controller with a derivative filter? (a) Repeat for the series PID controller with a derivative filter. (b) Simulate the time response of... The dynamic behavior of a temperature sensor / transmitter can be modeled as a first-order transfer function (in deviation variables) that relates the measured value T m to the actual temperature, T... If a certain amount of ideal gas occupies a volume V at STP on earth, what would be its volume (in terms of V) on Venus, where the temperature is 1003C and the pressure is 92 atm? (a) Using the process, sensor, and valve transfer functions in Exercise 11.21, find the ultimate controller gain K cu using a Bode plot. Using simulation, verify that values of K c > K cu cause... Use arguments based on the phase angle in frequency response to determine if the following combinations of G = G v G p G m and G c become unstable for some value of K c . a. b. c. d. e. |G = G. = K.... (a) Sketch the I C - V CE characteristics in the forward-active region for an npn transistor with β F = 100 (measured at low V CE ), V A = 50 V, BV CBO = 120 V, and n = 4. Use Where M is... What is the sheet resistance of a layer of 1 -cm material that is 5 mm thick? Consider a satellite in orbit about a spherically symmetric planet. If the orbit is circular, the sub-satellite point travels uniformly along its circular track. If the orbit is not circular,... Prove Equations (10.2) to (10.5). Equation 10.2 Equation 10.3 Equation 10.4 Equation 10.5 Av = 2GM RE R GM Av For the system of capacitors shown in Fig. E24.21, a potential difference of 25 V is maintained across ab. (a) What is the equivalent capacitance of this system between a and b? (b) How much charge... Two small stereo speakers A and B that are 1.40 m a part are sending out sound of wavelength 34 cm in all directions and all in phase. A person at point P starts out equidistant from both speakers... The electron in a hydrogen atom can be considered to be in a circular orbit with a radius of 0.0529 nm and a kinetic energy of 13.6 eV. If the electron behaved classically, how much energy would it... A process control engineer has decided to install an automated shower control system in a bathroom of her mansion. The design calls for a system that can deliver 3 gal/min of water at 110 F by... Find the acute angle between the two vectors A = 2a x + a y + 3a z and B = a x 3a y + 2a z by using the definition of (a) The dot product; (b) The cross product. Two point charges of 100C are located at (2, 1, 0) and (2, 1, 0). The surface x = 0 is a conducting plane. (a) Determine the surface charge density at the origin. (b) Determine S at P(0, h, 0). Obtain the complex exponential Fourier series coefficients for the (a) pulse train, (b) half-rectified sinewave, (c) full-rectified sinewave, and (d) triangular waveform as given in Table 2.1. Table... The positive portion of the envelope of the output of an AM modulator is shown in Figure 3.33. The message signal is a waveform having zero DC value. Determine the modulation index, the carrier... An FM modulator has output where f d = 20 Hz/V. Assume that m(t) is the rectangular pulse m(t) = 4II [1/8(t - 4)] (a) Sketch the phase deviation in radians. (b) Sketch the frequency deviation in... An FM modulator with f d = 10 Hz/V. Plot the frequency deviation in Hz and the phase deviation in radians for the three message signals shown in Figure 4.37. Figure 4.37 (0) 4 3 1 3 4 () () 3 3 2 2.5... Prove that J n (β) can be expressed as and use this result to show that J -n (β) = (-1) n J n (β) cos(B sin x )dx J(B) = Develop a computer program and use the program to verify the simulation results shown in Figures 4.24 and 4.25. Figure 4.24 Figure 4.25 80 Af = 40 Hz 60 ww Af = 45 Hz 20 Af = 35 Hz Af= 20 Hz -20 2 4 ... Determine the average power absorbed by each resistor in Figure 10.30. Lossless, v= 2c/3 Z, = 50 2 0.5/0 A 25 2 100 2 2.6 2 Space scientists have a large test chamber from which all the air can be evacuated and in which they can create a horizontal uniform electric field. The electric field exerts a constant horizontal... The characteristic impedance of a certain lossless transmission line is 72. If L = 0.5H/m, find (a) C; (b) p; (c) if f = 80 MHz. (d) The line is terminated with a load of 60 . Find and s. Determine the input resistance, transconduc-tance, output resistance, and maximum open-circuit voltage gain for the CE-CB circuit of Fig. 3.36 if I C1 = I C2 = 250 µA. Fig. 3.36: R. Q2 VBIAS... Determine the output current and output resistance of the circuit shown in Fig. 4.61. Fig. 4.61: + 15 V 13.7 k2 |'OUT Q2 700 2 For the common-drain amplifier of Fig. 3.73, assume W/L = 10 and λ = 0. Use Table 2.2 for other parameters. Find the dc output voltage V O and the small-signal gain ν o... For the circuit of Fig. 6.53, determine the output current as a function of the input voltage. Assume that the transistor operates in the active region. Figure 6.53 lout Ideal Vin
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